Logarithms exist to get the unknown out of the exponent. Everything in this topic follows from that one purpose, plus three laws that turn multiplication into addition and powers into multiplication.
Syllabus points covered
- Understand the relationship between logarithms and indices, and use the laws of logarithms
- Solve equations of the form aˣ = b
- Understand and use the definition and properties of eˣ and ln x
- Sketch graphs of exponential and logarithmic functions and their transformations
- Use logarithms to transform a relationship of the form y = kxⁿ or y = k(aˣ) to straight-line form
Common mistakes
- Writing log(a + b) as log a + log b. The law applies to products, not sums.
- Taking logs of both sides but only of one term when the equation has several.
- Losing the restriction that you cannot take the log of zero or a negative number — check solutions back.
- In straight-line-form questions, mixing up which variable is plotted on which axis after taking logs.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questionsComing soon
- Mark schemeComing soon
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Additional Mathematics past papers